Advertisements
Advertisements
Question
If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?
Advertisements
Solution
We have to find the unknown x using the distance between A( x , 0) and B ( 0 , 3 ) which is 5.In general, the distance between A`(x_1 , x_2 )` and B `(x_2 , y_2) ` is given by,
`AB = sqrt( ( x_2 - x_1 )^2 + (y_2 - y_1)^2)`
So,
`5 = sqrt ( ( x - 0)^2 + ( 0 -3 )^2 ) `
Squaring both the sides we get,
`x^2 - 16 = 0`
So,
`x = +- 4`
APPEARS IN
RELATED QUESTIONS
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
A (3, 2) and B (−2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates `(5/3,-1/3)`Find the coordinates of the third vertex C of the triangle.
Show that the following points are the vertices of a rectangle
A (0,-4), B(6,2), C(3,5) and D(-3,-1)
In what ratio does the point P(2,5) divide the join of A (8,2) and B(-6, 9)?
Find the ratio in which the point (-1, y) lying on the line segment joining points A(-3, 10) and (6, -8) divides it. Also, find the value of y.
Find the area of the quadrilateral ABCD, whose vertices are A(−3, −1), B (−2, −4), C(4, − 1) and D (3, 4).
The perpendicular distance of the P (4,3) from y-axis is
Show that the points (−4, −1), (−2, −4) (4, 0) and (2, 3) are the vertices points of a rectangle.
If (x, y) be on the line joining the two points (1, −3) and (−4, 2) , prove that x + y + 2= 0.
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
If three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
Write the ratio in which the line segment doining the points A (3, −6), and B (5, 3) is divided by X-axis.
If the distance between the points (3, 0) and (0, y) is 5 units and y is positive. then what is the value of y?
If P (2, p) is the mid-point of the line segment joining the points A (6, −5) and B (−2, 11). find the value of p.
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
If the points(x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
If the line segment joining the points (3, −4), and (1, 2) is trisected at points P (a, −2) and Q \[\left( \frac{5}{3}, b \right)\] , Then,
Seg AB is parallel to X-axis and coordinates of the point A are (1, 3), then the coordinates of the point B can be ______.
Co-ordinates of origin are ______.
